Question

How do you write `5x^(4/9)` in radical form?

Answer 1

See the solution process below:

Explanation:

First, we can use this rule of exponents to rewrite the expression:

`x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)`

`5x^(4/9) = 5x^(color(red)(4) xx color(blue)(1/9)) = 5(x^color(red)(4))^color(blue)(1/9)`

Now, we can use this rule of exponents to rewrite this expression in radical form:

`x^(1/color(red)(n)) = root(color(red)(n))(x)`

`5(x^4)^(1/color(red)(9)) = 5root(color(red)(9))(x^4)`